Question

How do you differentiate `f(x)=cosx(cotx)`?

Answer 1

Differentiating `f(x)` comes to be `-cosx((1+sin^2x)/sinx).`

Explanation:

Let, `y=f(x)=cosx*cotx`
Therefore Differentiating `y` w.r.t `x` comes to be,

`(dy)/(dx)=d/(dx)(cosx*cotx)`
`:.dy/dx=cosx*d/(dx)(cotx)+cotx*d/(dx)(cosx)`
`:.dy/dx=cosx*(-cosec^2x)+cotx*(-sinx)`
`:.dy/dx=-cosx/sin^2x-cosx=-cosx((1+sin^2x)/sinx).` (answer).